A Restricted Linearised Augmented Lagrangian Method for Euler's Elastica Model

A simple cutting-off strategy for the augmented Lagrangian formulation for minimising the Euler's elastica energy is introduced. It is connected to a discovered internal inconsistency of themodel and helps to decouple the tricky dependence between auxiliary splitting variables, thus fixing the problem mentioned. Numerical experiments show that the method converges much faster than conventional algorithms, provides a better parameter-tuning and ensures the higher quality of image restorations.

Automated summary

The introduced cutting-off strategy improves the efficiency of minimizing Euler's elastica energy, resolves internal inconsistencies in the model, and decouples complex dependencies between auxiliary splitting variables more effectively, leading to faster convergence and higher quality image restorations.